A measuring device for the contactless determination of the body temperature of a person, which comprises, on the one hand, a temperature sensor unit for the detection of a surface temperature of the person's body, is known from DE 10 2004 027 443 B3. On the other hand, the prior-art measuring device comprises an evaluating unit for evaluating the sensor signal detected by the temperature sensor unit and for calculating a current temperature signal, which is then visually reproduced in a downstream display unit. To enable a measurement to take place, it is necessary to accurately align the prior-art measuring device with the desired site of measurement on the body. Should the measuring device be aligned, for example, with cooler regions of the body or with the clothing of the person, undesired mismeasurements would occur. Furthermore, mismeasurements would also occur in case of incorrect alignment when the temperature sensor unit detects the temperature of heated respiration tubes, heated infusion tubes or parts of thermotherapy devices.